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February
Accounting forSubsoilMineral Resources
, A blue-ribbon panel of the National Academy
of Sciences’ National Research Council completed a congres-
sionally mandated review of the work that the Bureau of
Economic Analysis ()hadpublishedonintegratedeco-
nomic and environmental accounts. The panel’s final report
commended for its initial work in producing a set of sound
and objective prototype accounts. The November issue
of the S C B contained an article by
William D. Nordhaus, the Chair of the Panel, that presented
an overview of the major issues and findings and a reprint
of chapter , “Overall Appraisal of Environmental Accounting
in the United States,” from the final report. As part of its
promise to inform users of the results of this evaluation, is
reprinting additional chapters from the panel’s report; below
is a reprint of chapter ,whichreviews’s development of
a set of subsoilmineral accounts.
This article is reprinted with permission from Nature’s
Numbers: Expanding the National Economic Accounts to
Include the Environment. Copyright of the National Academy
Press, Washington, .ThisisareportoftheNational
Research Council, prepared by the Panel on Integrated Envi-
ronmental and Economic Accounting and edited by William
D. Nordhaus and Edward C. Kokkenlenberg.
INTRODUCTION
S
minerals—particularly petroleum,
natural gas, and coal—have played a key role
in the American economy over the last century.
They are important industries in themselves, but
they also are crucial inputs into every sector of
the economy, from the family automobileto mil-
itary jets. In recent years, the energy sector has
been an important contributor to many environ-
mental problems, and the use of fossil fuels is
high on the list of concerns about greenhouse
warming.
The National Income and Product Accounts
() currently contain estimates of the produc-
tion of mineral products and their flows through
the economy. But the values of and changes in
the stocks of subsoil assets are currently omit-
ted from the .Thecurrenttreatmentof
these resources leads to major anomalies and in-
accuracies in the accounts. For example, both
exploration and research and development gener-
ate new subsoilmineral assets just as investment
creates new produced capital assets. Similarly,
the extraction of mineral deposits results in the
depletion of subsoil assets just as use and time
cause produced capital assets to depreciate. The
include the accumulation and depreciation
of capital assets, but they do not consider the
generation and depletion of subsoil assets.
The omission is troubling. Mineral resources,
like labor, capital, and intermediate goods, are
basic inputs in the production of many goods and
services. The production of mineralresources is
no different from the production of consumer
goods and capital goods. Therefore, economic
accounts that fail to include mineral assets may
seriously misrepresent trends in national income
and wealth over time.
Omission of minerals is just one of the issues
addressed in the construction of environmental
accounts. Still, extending the to include
minerals is a natural starting point for the project
of environmental accounting. These assets—
which include notably petroleum, natural gas,
coal, and nonfuel minerals—are already part of
the market economy and have important links to
environmental policy. Indeed, production from
these assets is already included in the nation’s
grossdomesticproduct(). Mining is a signifi-
cant segment of the nation’s output; gross output
originating in mining totaled billion, or .
percent of ,in. Thisfiguremasksthe
importance of production of subsoil minerals in
certain respects, however, for they are intimately
linked to many serious environmental problems.
Much air pollution and the preponderance of
emissions of greenhouse gases are derived di-
rectly or indirectly from the combustion of fossil
fuels—a linkage that is explored further in the
next chapter. Moreover, while the value of min-
eral assets may be a small fraction of the nation’s
total assets, subsoil assets account for a large pro-
portion of the assets of certain regions of the
country.
Current treatment of subsoil assets in the U.S.
national economic accounts has three major lim-
itations. First, there is no entry for additions to
the stock of subsoil assets in the production or
asset accounts. This omission is anomalous be-
cause businesses expend significant amounts of
resources on discovering or proving reserves for
future use. Second, there is no entry for the using
up of the stock of subsoil assets in the production
February •
or asset accounts. When the stock of a valu-
able resource declines over time through intensive
exploitation, this trend should be recognized in
the economic accounts: if it is becoming increas-
ingly expensive to extract the subsoil minerals
necessary for economic production, the nation’s
sustainable production will be lowered. Third,
there is no entry for the contribution of subsoil
assets to current production in the production
accounts. The contribution of subsoil assets is
currently recorded as a return to other assets,
primarily as a return to capital.
There is a well-developed literature in
economics and accounting with regard to the ap-
propriate treatment of mineral resources. The
major difficulty for the national accounts has
been the lack of adequate data on the quanti-
ties and transaction prices of mineral resources.
Unlike new capital goods such as houses or com-
puters, additions to mineral reserves are not
generally reflected in market transactions, but are
determined from internal and often proprietary
data on mineral resources. Moreover, there are
insufficient data on the transactions of mineral
resources, and because these resources are quite
heterogenous, extrapolating from existing trans-
actions to the universe of reserves or resources is
questionable.
Notwithstanding the difficulties that arise in
constructing mineral accounts, the Bureau of
Economic Analysis () decided this was the
best place to begin development of its Integrated
Environmental and Economic Satellite Accounts
(). in the United States and compa-
rable agencies in other countries have in recent
years developed satellite accounts that explicitly
identify mineral assets, along with the changes in
these assets over assets, along with the changes in
these assets over time. This chapter analyzes gen-
eral issues involved in minerals accounting and
assesses the approach taken by (as described
in Bureau of Economic Analysis [b]). The
first section provides an overview of the nature of
subsoil mineralresources and describes the basic
techniques for valuing subsoil assets. The second
section describes ’s approach to valuation, in-
cluding the five different methods it uses to value
subsoil mineral assets. The third section high-
lights the specific strengths and weaknesses of
’s approach, while the fourth considers other
possible approaches. The chapter ends with con-
clusions and recommendations regarding future
efforts to incorporate subsoilmineral assets into
the national economic accounts.
GENERAL ISSUES IN ACCOUNTING FOR
MINERALRESOURCES
Basics of Minerals Economics
A mineral resource is “a concentration of
naturally occurring solid, liquid, or gaseous ma-
terial,inorontheearth’scrust,insuchform
and amount that economic extraction of a com-
modity from the concentration is currently or
potentially feasible” (Craig et al., :). The
size and nature of many mineralresources are
well known, whereas others are undiscovered and
totally unknown. Figure – shows a spectrum of
resources that differ in their degree of certainty,
commonly described as measured, indicated, in-
ferred, hypothetical, and speculative. Another
important dimension is the economic feasibil-
ity or cost of extracting and using the resources.
Some resources are currentlyprofitable to exploit;
others may be economical in the future, but cur-
rently are not. Along this dimension, mineral
resources are conventionally described as eco-
nomic (profitable today), marginally economic,
subeconomic, and other.
Resources that are both currently profitable to
exploit (economic) and known with considerable
certainty (measured or indicated) are called re-
serves (or ores when referring to metal deposits).
This means reserves are always resources, though
not all resources are reserves.
Over time, reserves may increase. Exploration
may result in the discovery of previously un-
known deposits or demonstrate that a known de-
posit is larger than formerly indicated. Research
and development may produce new techniques
that allow previously known but uneconomic
resources to be profitably extracted. A rise
in a mineral commodity’s price may also in-
crease reserves by making previously unprofitable
resources economic.
The exploration required to convert resources
into reserves entails a cost. As a result, compa-
nies have an incentive to invest in the generation
of new reserves only up to the point at which re-
serves are adequate for current production plans.
For many mineral commodities, therefore, re-
serves as a multiple of current extraction tend to
remain fairly stable over time.
. Two additional categories of mineral endowment are worth noting
since they are commonly encountered. The reserve base encompasses the
categories of reserves and marginal reserves, as well as part of the category
of demonstrated subeconomic resources shown in Figure –. While reserves
and the reserve base are typically a small subset of resources, resources in
turn are a small subset of the resourcebase. The resourcebase, not illustrated
in Figure –, encompasses all of a mineral commodity found in the earth’s
crust.
• February
While by definition all reserves can be exploited
profitably, the costs of extraction, processing, and
marketing, even for reserves of the same min-
eral commodity, may vary greatly as a result of
the reserves’ heterogenous nature. Deposit depth,
presence of valuable byproducts or costly impu-
rities, mineralogical characteristics, and access to
markets and infrastructure (such as deepwater
ports) are some of the more important factors
that give rise to cost differences among reserves.
Figure – reflects the heterogenous nature of
mineral resources by separating the reserves and
other known resourcesfor a particular mineral
commodity according to their exploitation costs.
The lowest-cost reserves are in class A ;their
quantity is indicated in the figure as
0A and their
exploitation costs as
0C
1
. The next least costly
reserves are found in class
B, with a quantity of
AB and a cost of 0C
2
. The most expensive re-
serves are found in class
M . These reserves are
. Similar comparative cost curves are used to illustrate the relative costs
of mineral production for major producing countries or companies. See, for
example, Bureau of Mines () and Torries (, ).
marginally profitable. The market price 0P just
covers the extraction cost of class
M (0C
m
)plus
the opportunity cost (
C
m
P) of using these re-
serves now rather than saving them for future
use. This opportunity cost, which economists re-
fer to as Hotelling rent (or sometimes scarcity rent
or user cost) is the present value of the additional
profit that would be earned by exploiting these
reserves at the most profitable time in the future
rather than now.
Known resources in Figure – with costs above
those of class
M , such as those in classes N , O ,
and
P, are by convention not reserves. In this
case, mineral producers, like other competitive
firms, will have an incentive to produce up to the
point where the current production costs of the
next unit of output, inclusive of rents, just equals
the market price. When Hotelling rents exist,
. Where the relevant market for a mineral commodity is global and
transportation costs are negligible, Figure – reflects cost classes for reserves
and other known resources throughout the world. Where a mineral com-
modity is sold in regional markets, a separate figure would be required for
each regional market, and the cost classes shown in any particular figure
are only for the reserves and other known resources in the regional market
portrayed.
February •
they are the same for all classes of reserves for a
particular mineral commodity market. Thus, the
total Hotelling rent shown in Figure – is simply
the Hotelling rent earned on marginal reserves
(
C
m
P) times total reserves (0M ).
Those reserves whose marginal extraction costs
are below those of the marginal reserves in class
M are called inframarginal reserves. As a result
of their relatively low costs, they yield addi-
tional profits when they are exploited. Mineral
economists refer to these additional profits as Ri-
cardian rents. In Figure –, the Ricardian rents
per unit of output equal
C
1
C
m
for reserves in
class
A , C
2
C
m
for reserves in class B,andsoon.
Unless technical or other considerations in-
tervene, mineral producers will generally exploit
first those reserves that have relatively low pro-
duction costs and thus high Ricardian rents (like
classes
A and B). This implies that the reserves
currently being extracted have lower costs than
the average of all reserves and that their Ricardian
rents are likely to be above average.
Since reserves by definition are known and
profitable to exploit, they are assets in the
sense that they have value in the marketplace.
Although mineralresources other than those
classified as reserves might have in-completely
defined characteristics (in terms of costs and
quantities) or be currentlyunprofitableto exploit,
they still may command a positive price in the
marketplace. Petroleum companies, for exam-
ple, pay millions of dollars for offshore leases to
explore for oil deposits that are not yet proved
reserves. Mining companies pay for and retain
subeconomic deposits. The option of develop-
ing such deposits in the future has a positive
value because the price may rise, or some other
developments may make the deposits economic.
Thus, a full accounting of subsoil assets should
consider not only reserves, but also other mineral
resources with positive market value. In the case
of reserves, market value may reflect Hotelling
rent, Ricardian rent, and option value.
In the
case of mineralresources other than reserves, a
positive market value is due solely to their option
value.
Key Definitions in Mineral Accounting
Changes in the value of the mineral stock
come about through additions, depletions, and
revaluations of reserves.
. The total value of reserves is V =
i
v
i
R
i
,wherev
i
is the unit
value of reserves in class
i(i= A,B, ,M ), and R
i
is the quantity of
reserves of class
i.
• February
• Additions aretheincreasesinthevalueof
reserves over time due to reserve augmenta-
tions. They are calculated as the sum of the
price of new reserves times the quantity of
new reserves for each reserve class.
• Depletions are the decreases in the value
of reserves over time due to extraction.
They are similar to capital consumption
(depreciation) and parallel the concept of
additions.
• Revaluations are changes in the value of
reserves due to price changes. They measure
the residual change in the value of reserves
after correcting for additions and depletions.
Techniques for Valuing Mineral Assets
As noted in the last section, the major challenge
in extending the national accounts to include
subsoil minerals is to broaden the treatment of
mineral assets to include additions and depletions
and to incorporate depletion in the production
accounts. This task involves estimating the value
of the subsoil assets. A specific subsoil asset con-
sistsofaquantityofamineralresourceandthe
invested capital associated with finding and de-
veloping that resource. Invested capital includes
physical structures such as roads and shafts, as
well as capitalized exploration and drilling ex-
penses. The total value of the subsoil assets
equals the sum of the value of the mineral and
the value of the associated capital (see Figure –
). Currently, U.S. national economic accounts
include the value of the associated capital, but
exclude the value of the mineral resource. One
of the goals of natural-resource accounting is to
estimate the total value of subsoil assets and to
separate this estimate into the value of the min-
eral and the value of the associated capital. An
additional goal is to track over time changes in
the value of the stock that result from additions,
depletions, and revaluations.
Three alternative methodologies are used in
valuing mineral resources: () transaction prices,
() replacement value, and () net present value.
In developing its mineral accounts, used one
version of the first method and four versions of
the third. This section explains the basic elements
of each approach.
Transaction Prices
The most straightforward approach to valuing
mineral resources relies on market transaction
prices. This is the standard approach used across
the national economic accounts for capital assets.
When resources of petroleum, copper, gold, and
other minerals are sold, the value of the transac-
tion provides a basis for calculating the market
value of the mineral component of the asset.
A close look at the transaction-prices approach
reveals, however, a number of difficulties that
need to be resolved. The major difficulty is that a
market transaction usually encompasses a num-
ber of assets and liabilities, such as the associated
capital (e.g., surface roads, shafts, and refining
operations), taxes, royalty obligations, and en-
vironmental liabilities. Because the transaction
usually includes not only the mineral resources,
but also associated capital, the value of the capital
must be subtracted to obtain the mineral value.
In addition, the property is usually encumbered
with royalty obligations to prior owners or to
owners of the land. Many mineral properties also
have associated environmental problems, such as
contaminated soils and water, and they may even
be involved in complicated legal disputes, such
as connection to a Superfund site with joint and
several liability. Some of these associated assets
and liabilities (such as mining structures) are true
social costs or assets, while others (such as royalty
obligations) are factor payments.
Another difficulty with using transaction prices
is the sporadic nature of the transactions. The
infrequency of the transactions, coupled with the
heterogeneity of the grade of the resource, makes
it difficult to apply the transaction price for one
grade or location of the resource to other grades
in other locations.
Because of the complex assortment of assets
and liabilities associated with transactions of
mineral resources, the price must be adjusted
to obtain the value of a resource. As noted
February •
above, the working capital and the associated
capital must be subtracted from the transaction
price, while any extrinsic environmental liabilities
should be added, as should any factor payments,
such as royalties or taxes, to obtain the value of
the underlying resource.
Box – provides an example of how to ad-
just the transaction price to obtain the market
value of a mineral resource for a hypothetical
sale involving the purchase of , barrels of
oil. In this example, the buyer pays million
for a property containing , barrels of oil,
and this is recorded as the transaction value. At-
tached to those reserves is a long-term debt of
. million; this liability must be added to the
purchase price. If the acquired reserves also in-
clude associated working capital of . million,
this amount must be deducted from the purchase
price. Correcting for these two items creates an
effective purchase price or market value of the
asset of . million.
An additional issue arises because of payments
such as future taxes and royalties. In acquiring
the above property, the new owner must, for ex-
ample, pay a percent overriding royalty to the
landowner. Such payments should be included
in the value of the resource even though they do
not accrue to the seller of the property. In the
example shown in Box –, future royalties and
taxes are assumed to have a present value of .
million. These payments introduce a major new
complication because taxes and royalties depend
on future production. Not only are they un-
certain, but they also cannot be easily estimated
from market or transaction data. One approach
is to adjust the transaction price by marking up
the value of the transaction by a certain amount.
Adelman and Watkins (:), for example, sug-
gest that percent be added to the “effective
purchase price” to account for transfers. After
adjusting for royalties, this yields a social asset
value for the above property of . million. The
final adjustment is for associated capital, which is
assumed tohave avalueof . million. After this
amount is subtracted, the estimated social value
of the underlying petroleum reserve is calculated
to be . million.
Replacement Value
A second approach uses the costs of replacing
mineral assets to determine their value. Under
this approach, it is assumed that firms have an
incentive to undertake investments to find new
resources up to the point where the additional
cost of finding one more unit just equals the price
Box –: Transaction Price Method
a
Recorded Dollar Transaction (,
barrels) . million
Adjustments
Add: assumed liabilities . million
Subtract: working capital . million
Effective Purchase Price of Asset . million
Add: present value of taxes, royalty
transfers . million
Value of Assets . million
Subtract: value of associated capital . million
Value of Petroleum Reserve . million
a
This methodology is not followed in the conventional accounts. For
instance, in valuing the stock of cars, we do not subtract tax credits, nor
do we add in future liabilities such as property taxes. Similarly, to the
extent that royalties are regarded as a sharing of profits (like dividends),
they should not affect the value of an asset; to the extent that royalties
are actually a deferred part of the purchase price, they can be capitalized
to increase the value of an asset.
Box –: Definitions of Symbols and Basic Concepts in Minerals
Accounting
For this discussion, assume that there is only one class of a mineral reserve,
that extraction costs are constant, and that the unit value of the reserve rises
at the social rate of discount. Variables are:
R
t
= total quantity of reserves of the mineral commodity at year end
H
t
= unit value of the reserves (say, petroleum reserves), which equals
Hotelling rent under the above assumptions
A
t
= quantity of new reserves discovered during the year
q
t
= quantity of extraction or production during the year
V
t
= total value of the reserves at year end
In a given year, petroleum firms might discover new reserves totaling
A
t
.
Then the additions are given by:
additions
t
= H
t
A
t
(.)
During that year, petroleum production, and therefore depletion of existing
reserves, is measured by
q
t
. Depletion is, under the special assumptions listed
above, quantity times the value of reserves:
depletions
t
= H
t
q
t
(.)
The total value of reserves at year end is:
value of reserves = V
t
= H
t
R
t
(.)
The change in the value from the end of year t − 1 to the end of year t is
given by:
change in value of reserves
= V
t
− V
t−1
= H
t
R
t
− H
t−1
R
t−1
(.)
Revaluations are the change in the value corrected for the value of additions
and depletions:
revaluation
= H
t
R
t
− H
t−1
R
t−1
− H
t
A
t
+ H
t
q
t
(.)
• February
at which firms can buy that unit—that is, up
to the market value. Therefore, the additional
or marginal cost of finding a mineral resource
should be close to its market price. Associated
with this approach, however, are many of the
same issues discussed above under transaction
prices. For example, a particular replacement
cost is relevant only for valuing deposits of com-
parable quality and cannot be used to value
resources of another grade. This point can be
illustrated using Figure –. Assume that explo-
ration is resulting in the discovery of resources
of class
M . The market value of this class would
be a function of the difference between
0P and
production cost
0C
M
. It would be profitable
for firms to continue exploring for such deposits
until the finding costs (that is, the replacement
costs) just reached the value of this class of re-
source. However, the replacement cost of class
M cannot be used to value other classes, such as
class
A , which have a lower extraction cost and
therefore a higher value. Because of cost differ-
ences, using class
M to value classes A through
L would yield an underestimate of the value of
these reserves.
Net Present Value
A third valuation technique, the net present
value or method, entails forecasting the
stream of future net revenues a mineral re-
source would generate if exploited optimally,
and then discounting this revenue stream using
an appropriate cost of capital.
Under certain
conditions—such as no taxes—the sum of the
discounted revenue values from each time pe-
riod will equal the market value of the resource.
For example, assume that a million-ounce
gold asset generates a stream of net revenues (af-
ter accountingfor all extraction and processing
costs) that, when discounted at a rate of per-
cent per year, has a present value of . billion.
According to this approach, the value of the as-
set is taken to be . billion. If the value of the
plant, equipment, and other invested capital ul-
timately associated with the asset is estimated to
be million, the current value of the gold re-
serves is billion, and their unit value is per
ounce. Again, as with the previous two methods,
each class of resource should be separately val-
ued, since the stream of revenues from a higher
class of resource will be greater than that from a
lower class.
. The appropriatediscount rate for energy and environmental resources
is debatable. See Lind (, ) , Schelling () , and Portney and
Weyant ().
A special case of the approach, known as
the Hotelling valuation principle (see Miller and
Upton, ), avoids the difficulties of forecasting
future net revenues and then discounting them
back to the present. This approach makes the
strong and generally unrealistic assumption that
the unit value of a resource grows at exactly the
same rate as the appropriate discount rate. In the
above example, this would imply that the unit
value of the gold resource would grow at the dis-
count rate of percent per year; that is, the
unit value would be in the first year, in
the next year, . in the following year, and so
forth. Under this assumption, the present value
of the resource would easily be calculated as the
current period’s resource price multiplied by the
current physical stock of the resource. Under a
further set of assumptions, such as homogeneous
resources and constant extraction costs, the cur-
rent period resource price is simply the current
net revenue (unit price less unit extraction cost).
For example, assume that in a given year the
United States has million ounces of homo-
geneous gold reserves, that the price of gold in
that year is per ounce, and that the av-
erage extraction cost is per ounce. Under
the Hotelling valuation principle, the price of the
gold reserves would be per ounce, and the
total value of the gold assets would be calculated
as . billion. Note that it would still be neces-
sary to deduct the value of capital from the .
billion to obtain the value of the mineral reserve.
Again, for this approach to be valid, the per unit
price of gold reserves ( in this example) would
need to grow at the discount rate appropriate for
these assets.
BEA’S VALUATIONOF SUBSOIL
MINERALS
This section presents a more detailed description
of ’s valuationmethods (as set forth in Bureau
of Economic Analysis, b). In the absence of
observable market prices for reserves, esti-
mates mineral reserve and flow values using five
valuation methods. These calculations are per-
formed for reserves of fuel minerals (petroleum,
natural gas, and coal) and other minerals (ura-
nium, iron ore, copper, lead, zinc, gold, silver,
molybdenum, phosphate rock, sulfur, boron, di-
atomite, gypsum, and potash) for each year from
through (oil and gas figures are calcu-
lated from to ). In addition, aggregate
stock and flow values for five mineral categories
(oil, gas, coal, metals, and other minerals) are en-
February •
tered in the appropriate rows and columns of the
Asset Account for . This section first
examines the five methods used by in esti-
mating mineral values, along with the data they
require, and then describes ’s findings. Box
– provides definitions of the symbols used in
minerals accounting.
BEA’sFive Basic Valuation Methods
Current Rent Method I
Current rent methods I and II are methods
based on the Hotelling valuation principle. The
attraction of the Hotelling valuation principle
is the ease with which the calculation can be
performed, avoiding the need to forecast min-
eral prices and to assume an explicit discount
factor. In both methods, the value of the ag-
gregate stock is calculated as the net price times
the quantity of reserves, where the net price is
as described below. Additions or depletions are
similarly calculated as net price times the quantity
of additions or depletions. One of the difficulties
with this approach is that the Hotelling valuation
principle tends to provide a systematic overvalua-
tion of reserves, the reason for which is discussed
in a later section.
Current rent methods I and II are quite simi-
lar in construction. They differ primarily in the
method of adjusting for the value of associated
capital. (The algebra of the different formulas is
shown in the boxes in this section.) Current rent
method I (see Box – ) uses the normal rate of
return on capital to determine the return on asso-
ciated capital in the mining industry that should
be subtracted from revenues. It then calculates
the “resource rent per unit of reserve” by taking
the net profits from mining, subtracting the re-
turn and depreciation on the associated capital,
and dividing that sum (called “resource rent” by
) by the quantity of resource extracted during
the year. The method thus yields an estimate of
the unit value of the reserves currently extracted.
To calculate the total value of the mineral
reserve, the current resource rent per unit is mul-
tiplied by the total reserves, in the spirit of the
Hotelling valuation principle. Additions and de-
pletions are calculated as those quantities times
the resource rent per unit. Revaluations are sim-
ply the residual of the change in the value of the
stocks plus depletions minus additions. It has
been observed that the value of the stock can be
highly volatile; this volatility is due primarily to
the revaluation effect.
Box –: Formulas for Current Rent Method I
total mineral reserve value
t
= V
t
=
[p
t
− a
t
]R
t
− rR
t
K
t
/q
t
− R
t
D
t
/q
t
=
[p
t
− a
t
− rK
t
/q
t
− D
t
/q
t
]×R
t
additions
t
= [p
t
− a
t
− rK
t
/q
t
− D
t
/q
t
]×A
t
depletions
t
= [p
t
− a
t
− rK
t
/q
t
− D
t
/q
t
]×q
t
revaluations
t
= V
t
− V
t−1
+ depletions
t
− additions
t
where
V
t
= value of mineral reserves
p
t
= price of commodity
a
t
= average cost of current production
R
t
= total quantity of reserves
r = average rate of return on capital
K
t
= value of associated capital, valued at current replacement cost
q
t
= total quantity extracted
D
t
= depreciation of associated capital
A
t
= quantity of discoveries of new reserves
additions
t
= value of discoveries of new reserves
depletions
t
= value of depletions
revaluations
t
= change in value of reserves corrected for depletions and
additions
The revaluation term is not directly calculated; it will include any errors in
calculating additions, depletions, and opening and closing stock values.
Current Rent Method II
Current rent method II is virtually identical to
current rent method I. The only difference is in
the method of adjusting for associated capital.
The value of the associated capital is subtracted
from the total value of the mineral asset to obtain
mineral-reserve values in current rent method
II. Again employing the Hotelling valuation ap-
proach, the total value of the mineral asset
(including the value of the associated capital) is
calculated as the per unit net revenue times the
total quantity of reserves. The total value of
the mineral reserve is then calculated as the to-
tal value of the asset value minus the value of
the associated capital. The unit resource value,
which is used to price additions and depletions,
is just this total reserve value divided by the to-
tal quantity of reserves. This approach is defined
algebraically in Box – .
As is discussed below, both current rent
methods have major advantages in that they are
easy to calculateon the basis of data currently
uses in its accounts (primarily profits and capital
stock and consumption data). They both suffer
from the serious disadvantage that they rely on
• February
Box –: Formulas for Current Rent Method II
total mineral reserve value
t
= V
t
=
[p
t
− a
t
− K
t
/R
t
]R
t
additions
t
= [p
t
− a
t
− K
t
/R
t
]×A
t
depletions
t
= [p
t
− a
t
− K
t
/R
t
]×q
t
revaluations
t
= V
t
− V
t−1
+ depletions
t
− additions
t
where variables are as defined in Box ..
the Hotelling valuation principle, thereby tending
to overvalue reserves.
Net Present Value Estimates
If the basic assumptions of the Hotelling
valuation principle do not hold—and there is
strong evidence that they do not, as discussed
below—life becomes much more complicated
for national accountants. One approach that
is sound from an economic point of view is
to value reserves by estimating the present dis-
counted value of net revenues. To render the
present value approach workable, makes
three simplifying assumptions. First, it assumes
that the quantity of extractions from an addition
to proved reserves is the same in each year of
a field’s life. The quantity of depletions in any
year is assumed to result equally from all vin-
tages (cohorts) still in the stock, i.e., all vintages
whosecurrentageislessthantheassumedlife.
Second, the life for a new addition is assumed
to be years until and years thereafter.
Third, assumes that the discount rate applied
to future revenues is constant at a rate of either
percent per year or percent per year above
the rate of growth of the net revenues (where the
latter equals the rate of growth of the price of the
resource).
These assumptions lead to a tractable set of
calculations. The present discounted value of
the mineral stock as calculated using this present
value method is simply the stock and flow values
calculated with current rent method II, multi-
plied by a “discount factor” of between . and
. for the percent discount rate and between
. and . for the per cent discount rate.
. According to , the rates were chosen to illustrate the effects of a
broad range of approaches. The percent per year discount rate has been
used by some researchers to approximate the rate of time preference, while
the percent rate has been used by some researchers to approximate the
long-term real rate of return to business investment.
.Atthe percent discount rate, the . discount factor holds for the
years through , with the rate edging upward thereafter as a result
of commingling of reserves that were developed prior to (which
assumes are extracted over years) with those developed in or later (for
The calculated values are, then, lower than the
values derived using current rent method II, with
the difference depending on the discount rate
employed.
Additions and depletions are then calculated
in a manner similar to that used with current
rent method II. The average unit reserve value
is calculated by dividing the total reserve value
by the quantity of reserves, and then using this
unit value to value additions and depletions.
Additions would be calculated as percent of
the value of additions according to current rent
method II if the discount rate is percent per
year, and percent of the value of additions
according to current rent method II if the dis-
count rate is percent. The calculated value
of depletions would be percent of the value
of depletions under current rent method II at a
percent discount rate, and percent at a
percent discount rate.
In summary, the present value method as im-
plemented by takes the values of additions,
depletions, and stocks calculated according to
current rent method II and multiplies them by
discount factors of between and percent.
The reason for the discount is straightforward.
Under current rent method II, which relies on the
Hotelling valuation principle, it is assumed that
net revenues rise at the discount rate. Under the
present value approach, net revenues are assumed
to rise at rates that are or percent slower
than the discount rate applicable to mineral as-
sets. The higher percentage is the discrepancy
between the rise in net revenues and the discount
rate; the lower is the discount factor. The
approach is shown in Box – .
Replacement Cost
The fourth method of calculating the value of
the mineral stock is used only for oil and gas re-
serves. Despite its name, this approach is similar
to the method, not to the replacement cost
method described earlier. It adopts the approach
of Adelman (), who calculates the present
value of an oil field using special assumptions. It
is assumed that the production from an oil or gas
field declines exponentially over time. Under the
assumption that the decline rate is constant and
which a -year life is assumed). For the percent discount rate, the .
factor holds for the years through .In, the year for which
calculates a more complete set of satellite accounts, the rate is . for the
percent discount rate and . for the percent discount rate.
. As with the calculation of mineral values, the factorsshown in Box –
vary depending on the year of the analysis. The factors reported are those for
the calculation. The factors differ in the various formulas because of the
differing treatment of the timing of depletions and additions from reserves.
February •
that the net revenue rises at a fixed constant rate
that is less than the discount rate, a barrel fac-
tor is calculated. This barrel factor is multiplied
times net revenue to obtain the present value of
the reserves. Adelman estimates that the barrel
factor is usually around .. does not give
the barrel factor used in its calculations, which
should vary by deposit and depend on the rate at
which future cash flows are discounted, but we
estimate that it averages approximately ..
The value of the asset—calculated with current
rent method II using the Hotelling valuation
principle—is then multiplied by the barrel fac-
tor. The justification is that this approach,
unlike the Hotelling approach, takes the physical
specifics of oil and gas extraction into account
and accordingly adjusts the unit value of re-
serves downward. As with the approach
discussed in the last section, this adjustment
accounts for the overvaluation inherent in the
Hotelling valuation principle.
Once the value has been adjusted downward,
must again subtract the value of capital as-
sociated with the asset. With this method, the
value of capital associated with each unit of ex-
isting reserves is assumed to be the current-year
expenditure on exploration and development for
oil and gas, divided by the quantity of oil and
gas extracted during the year. This approach is
loosely based on Adelman’s suggestion that the
value of capital associated with a unit of pro-
duction can be approximated by measuring the
value of capital associated with finding new re-
serves. The replacement cost method is shown
in Box – .
Transaction Price Method
When oil and gas firms desire additional reserves,
they can either buy them from other firms or find
new ones through exploration and development.
In the absence of risk, taxes, and other com-
plications, the transaction price of purchasing
new reserves should represent the market value
of those reserves. For this reason, according to
, “if available, transaction prices are ideal for
valuing reserves” (Bureau of Economic Analysis,
b:).
In fact, transactions in reserves are few and far
between outside of oil and gas, and even in oil
and gas suffer from problems discussed above.
To estimate transaction prices, derivedprices
from publicly available data on the activities of
large energy-producing firms for the period
to . The gross value of reserves was estimated
by dividing expenditures for the purchase of the
Box –: Formulas for Net Present Value Method
total mineral reserve value
t
@ percent discount rate=
0.88[p
t
− a
t
]R
t
− 0.88K
t
total mineral reserve value
t
@ percent discount rate =
0.69[p
t
− a
t
]R
t
− 0.69K
t
additions
t
@ percent discount rate=0.84[p
t
− a
t
− K
t
/R
t
]×A
t
additions
t
@ percent discount rate =0.59[p
t
− a
t
− K
t
/R
t
]×A
t
depletions
t
@ percent discount rate =0.83[p
t
− a
t
− K
t
/R
t
]×q
t
depletions
t
@ percent discount rate =0.60[p
t
− a
t
− K
t
/R
t
]×q
t
revaluations
t
= V
t
− V
t−1
+ depletions
t
− additions
t
where variables are as defined in Box –.
Note: The numerical values in this box apply to . As explained in the
text, slightly different values will apply for different years.
Box –: Formulas for Replacement Cost Method
total mineral reserve value
t
= V
t
=
{0.375[p
t
− a
t
]−Z
t
/q
t
}R
t
additions
t
= {0.375[p
t
− a
t
]−Z
t
/q
t
}×A
t
depletions
t
= {0.375[p
t
− a
t
]−Z
t
/q
t
}×q
t
revaluations
t
= V
t
− V
t−1
+ depletions
t
− additions
t
where Z
t
= value of exploration and development ex-
penditures in year
t, and other variables are as defined
in Box –.
Box –: Formulas for Transaction Price Method
total mineral reserve value
t
= V
t
=
(T V
t
/T Q
t
− K
t
/R
t
)R
t
additions
t
= (T V
t
/T Q
t
− K
t
/R
t
)×A
t
depletions
t
= (T V
t
/T Q
t
− K
t
/R
t
)×q
t
revaluations
t
= V
t
− V
t−1
+ depletions
t
− additions
t
where TV
t
= value of reserve transactions, and TQ
t
=
total quantity of reservestransacted, and other variables
are as defined in Box –.
rights to the proved reserves by the quantity of
purchased reserves. The result was then adjusted
for associated capital using the same method as
[...]... stock of minerals is for assessing trends in mineral scarcity In quantity terms, increasing scarcity might be reflected in a declining constant-dollar stock of mineralresources or of some component of mineralresources On this front, is developing a constant--price series formineral stocks, shown in Figure –, that is equivalent to a physical quantity series, aggregated across different mineral. .. prefer El Serafy’s concept of sustainability to other accounting conventions can make their own adjustments to national output using the information contained in satellite accounts CONCLUSIONS AND RECOMMENDATIONS ON ACCOUNTINGFORSUBSOILMINERALRESOURCES Appraisal of Efforts . should be commended for its initial efforts to value mineralsubsoil assets in the United States At very limited cost,... and will be useful for policy makers and analysts in the private sector . Because of the preliminary nature of the estimates, as well as the potential volatility introduced by the inclusion of mineral accounts, the panel recommends that continue to present subsoilmineral accounts in the form of satellite accounts for the near term Once the accounting procedures used for the mineral accounts... valuable minerals Development of reserve prices and unit values would help in assessing trends in resource scarcity Comprehensive mineral accounts would provide the information needed for sound public policies addressing public concerns related to mineralresources . Efforts to develop better mineralaccounting procedures domestically and with other countries would have substantial economic benefit for. .. April:– Bureau of Economic Analysis b Accountingformineralresources S C B April:– Bureau of Mines Minerals Yearbook , Vol II Washington, : U.S Department of the Interior Bureau of Mines An Appraisal of Minerals Availability for Commodities Washington, : U.S Department of the Interior Cairns, R.D Accountingfor Resource Depletion Unpublished paper,... up The real prices of individual mineral commodities provide a more direct and appropriate measure of recent trends in resource scarcity than is offered by the total values of specific minerals in the mineral accounts . The panel recommends that maintain a significant effort in the area of accountingfor domestic mineral assets While subsoil assets currently account for only a small share of total... for five types of mineral assets, including three types of fuels, and an aggregate mineral category This level of detail makes the satellite accounts useful to policy makers who wish to focus on particular mineral issues The data on the value of mineral stocks, additions, depletions, and revaluations (the residual) are given annually for the – period for oil and gas (the two most important mineral. .. is therefore clearly feasible and relatively inexpensive Consistency with Other Valuation and Accounting Frameworks treats mineral additions in parallel with other forms of capital formation In this respect, the U.S accounts differ from the System of Integrated Environmental and Economic Accounting (), an alternative satellite accounting system proposed by the United Nations In both accounting. .. employed by —that of relying on financial information for individual firms At the level of the firm, the value of mineral reserves can be imputed from data on financial balance sheets Figure – indicates the calculations required This method calculates a nation’s mineral wealth by aggregating the values of the domestic mineralresources held by all resident mineral firms This is a laborious process that... approach to accountingforsubsoil minerals We begin with the advantages of the approach and then review some issues and concerns Advantages Feasibility Phase I of ’s plan for extending the national accounts to include supplemental mineral accounts is now complete In accordance with the recommendations of the United Nations System of National Accounts (), limited the focus of Phase I to mineral . incorporate subsoil mineral assets into
the national economic accounts.
GENERAL ISSUES IN ACCOUNTING FOR
MINERALRESOURCES
Basics of Minerals Economics
A mineral. correctly accounting for mineral stocks
and flows in a set of satellite accounts will be
just as intensive an accounting exercise as current
accounting for the